And Neelix, since he could draw on Tuvok's long friendship with Janeway, would have understood that she wouldn't just throw him unceremoniously off the ship.
I guess we're supposed to assume that most of their memories as Tuvix were lost upon separation.
I thought they did retain their memories as Tuvix. The scene with both of them sitting on the sickbay bed would seem to bear this out.
At the very least, I would think that - given how different Tuvok and Neelix are - they would be grateful for being separated again. The thought of being combined probably would make BOTH of them sick.